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Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u factor...

Price a put option with a one-step binomial tree. Suppose So=50, X=40, 1+r=1.06. The u factor is 1.4 and the d factor is 0.6. Show the steps. (12 points)

Solutions

Expert Solution

c0= Call price = [c1+ + (1-)c1- ]/ (1+r)
p0= Put price = [p1+ + (1-)p1- ]/ (1+r)
Where
∏= Risk neutral probability = (1+r-d)/(u-d)
r= risk free interest rate = 6%
u= up factor = 1.4
d= Down factor = 0.6
∏= Risk neutral probability = (1+0.06-0.6)/(1.4-0.6)
=                          0.5750
1- ∏= =                          0.4250
S0 = Stock price today = 50
S1+ = = 50 × 1.4 =                            70.00
S1- = = 50 × 0.6 =                            30.00
X = Exercise price = 40
p1+ = = Max(0, X - S1+)
= Max(0, 40 - 70) = 0
p1- = = Max(0, X - S1-)
= Max(0, 40 - 30) =                       10.0000
p0= (0.575 × 0 + 0.425 × 10) /(1+0.06 ) = 4.01

Fair value of put option is $4.01

please rate.


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